GEODESIC STARS IN RANDOM GEOMETRY

• 成果类型: Article
• 署名作者: Le Gall, Jean-Francois
• 署名单位: Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1553
• 发表日期: 2022
• 页码: 1013-1058
• 关键词: scaling limit; planar maps

摘要

A point of a metric space is called a geodesic star with m arms if it is the endpoint of m disjoint geodesics. For every m is an element of {1 , 2, 3, 4}, we prove that the set of all geodesic stars with m arms in the Brownian sphere has dimension 5 - m. This complements recent results of Miller and Qian, who proved that this dimension is smaller than or equal to 5 - m.